Linear Regression
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Linear Regression
Linear regression is a way to find the line that best represents a data set that is approximately linear. In this lesson, you will learn how to use a TI-84 calculator to fit a line to a data set, find the equation of the line, and use it to make predictions.
Linear regression is a way to find the line that best represents a data set that is approximately linear. In this lesson, you will learn how to use a TI-84 calculator to fit a line to a data set, find the equation of the line, and use it to make predictions.
Linear Regression
Before You Begin
Press the button that says STAT. Select number 5: SetUpEditor and press ENTER. Press ENTER again. The home screen should display Done. This clears all entries from your calculator's lists.
Press the Y= button and delete any entries you see. Make sure Plot1, Plot2 and Plot3 are not highlighted. This clears any graphs you may have.
You are ready to begin!
Press the button that says STAT. Select number 5: SetUpEditor and press ENTER. Press ENTER again. The home screen should display Done. This clears all entries from your calculator's lists.
Press the Y= button and delete any entries you see. Make sure Plot1, Plot2 and Plot3 are not highlighted. This clears any graphs you may have.
You are ready to begin!
Before You Begin
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Plotting the Data Set
Press STAT and select 1: Edit... In L1, enter the values of your your independent variable (x-values). Put the values of your dependent variable (y-values) in L2.
Press 2nd STAT PLOT (above Y=). 1: Plot1 will be highlighted. Press ENTER. On will be flashing. Press ENTER again. Notice that the options say Xlist:L1 and Ylist:L2. You can leave all the options as they are.
Press GRAPH. If you do not see anything, press ZOOM and select 9: ZoomStat. This option will choose a viewing window that is appropriate for your data.
Press STAT and select 1: Edit... In L1, enter the values of your your independent variable (x-values). Put the values of your dependent variable (y-values) in L2.
Press 2nd STAT PLOT (above Y=). 1: Plot1 will be highlighted. Press ENTER. On will be flashing. Press ENTER again. Notice that the options say Xlist:L1 and Ylist:L2. You can leave all the options as they are.
Press GRAPH. If you do not see anything, press ZOOM and select 9: ZoomStat. This option will choose a viewing window that is appropriate for your data.
Plotting the Data Set
WAIT!
At this point, it is very important to ask yourself: "Does my data set look approximately like a line?"
If the answer is "No," do not proceed. Linear regression is not appropriate for your data.
At this point, it is [b]very important[/b] to ask yourself: "Does my data set look approximately like a line?"
If the answer is "No," [b]do not proceed[/b]. Linear regression is not appropriate for your data.
WAIT!
Finding the Line of Best Fit
Press STAT. Move your cursor right to highlight CALC. Select 4: LinReg(ax+b) [which stands for "linear regression in slope-intercept form"] and press ENTER. You will see this text on the home screen. Press VARS and move your cursor right to highlight Y-VARS. Select 1: Function and press ENTER. Select 1: Y1 and press ENTER again. Press ENTER one last time. Your regression equation will appear on the screen.
...but wait, there's more!
Press the Y= button. You will see your regression equation in Y1. Press GRAPH. There is your data set...and there is the line of best fit, just like magic!
Press STAT. Move your cursor right to highlight CALC. Select 4: LinReg(ax+b) [which stands for "linear regression in slope-intercept form"] and press ENTER. You will see this text on the home screen. Press VARS and move your cursor right to highlight Y-VARS. Select 1: Function and press ENTER. Select 1: Y1 and press ENTER again. Press ENTER one last time. Your regression equation will appear on the screen.
[em]...but wait, there's more![/em]
Press the Y= button. You will see your regression equation in Y1. Press GRAPH. There is your data set...and there is the line of best fit, [em]just like magic![/em]
Finding the Line of Best Fit
Predicting the Future
You can use your regression equation to predict where new data points not included in your data set will lie. For example, suppose your data set gave the world population in 1990, 1995, 2000 and 2005. You have found a regression equation for the data, stored it in Y1, and now you want to use it to predict the world population in 2010 (or 2011 or 2050...)
On the home screen, press VARS and move your cursor right to highlight Y-VARS. Select 1: Function and press ENTER. Select 1: Y1 and press ENTER again. You will see Y1 on your home screen. After it, type (2010) and press ENTER. Your calculator will plug the value 2010 into the regression equation stored in Y1 and give you the predicted value of the world population in 2010!
You can use your regression equation to predict where new data points not included in your data set will lie. For example, suppose your data set gave the world population in 1990, 1995, 2000 and 2005. You have found a regression equation for the data, stored it in Y1, and now you want to use it to predict the world population in 2010 (or 2011 or 2050...)
On the home screen, press VARS and move your cursor right to highlight Y-VARS. Select 1: Function and press ENTER. Select 1: Y1 and press ENTER again. You will see Y1 on your home screen. After it, type [tt](2010)[/tt] and press ENTER. Your calculator will plug the value 2010 into the regression equation stored in Y1 and give you the predicted value of the world population in 2010!
Predicting the Future
Print
Set Notation 
Order of Operations 
